# 5.1.3 Forces as Vectors

### Forces as Vectors

• Forces are vector quantities as they are described by both magnitude and direction
• The magnitude of a force is measured in Newtons
• The direction of a force can be described as left, right, up, down or even using angles A free body diagram of an object with two forces acting on it

• The direction of a force can be imagined using a number line
• Numbers to the left of zero are negative as are forces pointing left
• Numbers to the right of zero are positive as are forces pointing right Vectors represented as positive or negative vectors depending on their direction

• Not all forces are directed perfectly horizontally or vertically and thus need to have an angle described
• It is useful to describe an angle with respect to the vertical or the horizontal A force of magnitude 100 N directed 40° to the horizontal

### Force Pairs

• When there is an interaction between two objects, a force is exerted on each object
• This is known as a force pair
• Examples of these force pairs include:
• The downwards force due to the weight of a laptop resting on a desk, the desk exerts a normal force back up on the laptop
• The force exerted by a basketball player throwing a basketball is opposed by the reaction force of the basketball on the player
• The tension force exerted along a cable to a suspended object is opposed by the force of the weight of the object
• Force pairs can be represented by arrows in vector diagrams The force pairs present with respect to a rock being pushed by a person

• The applied force that the person exerts on the rock is opposed by a reaction force from the rock
• The weight of the rock on the ground is opposed by a normal force
• The weight of the person is also opposed by a normal force
• The force applied by the person driving their feet into the ground is opposed by friction ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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